I want to install a flat screen TV wall mount (full motion kind) into 1/4' drywall with 2x4 studs. There will be 4 attachment points, to studs 24" apart. Total weight of the wall mount and the TV will be 75 lbs. Is this a good idea?
TV wall mounts should always be mounted directly onto studs if the total weight is that much. If all mounting screws are going into studs, the drywall thickness is irrelevant. Drywall anchors are a great invention, but not suited for the kinds of load and forces a swivel wall mount exerts.
If you can't mount the wall mount onto studs for some reason (like, say, because the studs are spaced 24" and the mounting screws on the wall mount are <24" apart), mount a length of 2x4 lumber onto the wall and secure it onto the studs. Then mount your tv wall mount onto the 2x4. I suggest 2 strips - one for the upper and lower rows of mounting screws.
And of course read the instructions that come with the wall mount to see if they have specific recommendations for dealing with your situation.